Curriculum Vitae for Marius Crainic

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activities, final ceremony, etc), to attract new MC proposals, to advertise the program, to select the students etc. Master Classes coordinated: – Arithmetic Geometry and Noncommutative Geometry (2009-2010) – Numerical Bifurcation Analysis of Dynamical Systems (2009-2010) – Calabi-Yau geometry (2008-2009) – Quantum groups, affine Lie algebras and applications (2007-2008) – Symplectic geometry and Beyond (2006-2007) (Also Scientific organizer). – Logic (2006-2007). – Finite and infinite dimensional dynamical systems (2005-2006). – Stochastics in Molecular Biology and Genetics (2004-2005). There are several main achievements in this direction: – During this period, the Master Class obtained the financial support of the various dutch clusters (most notably, the GQT cluster supports each year about 8 students, for a period of 6 years). The survival of the Master Class depends on finding such financial support. – The Master Class program made it into the academic news (when, at the opening of the GQT cluster, the Ministry of Education spoke about the importance of the MC and handed out to the students their diplomas). – As a step in advertising the programme, I made a new data-base (up-to-date and complete) containing the main Mathematics Departments around the world and their addresses. This data base is nowadays used by the entire department for advertising various other programs. – I started another data-base, containing the names and the whereabouts of the former Master Class students. This information was already used by NWO in some of their public presentations (serving as an interesting analysis from various points of view: the role of foreign students coming and studying in Holland, the extremely varied career paths taken by them). • Stafcolloquium (UU) (2004-2008): Organizer of the general (weekly) Stafcolloquium of the Mathematics Department, Utrecht University, together with G. Cornelissen (until 2006/2007) and with R. Bisseling (remaining period). The duties include the process of finding and inviting speakers, managing the Stafcolloquium funds, etc. • Memberships, committees: - Member of the national research commission (“Commissie Onderzoek”) of the PWN (since 2010). - Editor for the journal Indagationes (since 2010). - Editor for the journal Mathematica (since 2009) - Part of various selection committees, such as the one for the UD position at UU associated to the GQT cluster (2008), or the Vrije Competitie selection committees for 2010 and 2012. 12
The broad research interests of Marius Crainic: Geometry and Topology Geometry is the oldest branch of mathematics. It is concerned with questions of shape, size, relative position of figures, and the properties of space. Its empirical origins were put into an axiomatic form by Euclid (3rd century BC ), and the resulting Euclidean geometry has been standard for many centuries. Questions from astronomy, on the position and the movement of stars and planets, served as an important source of geometric problems during one and a half millennia. The discovery of coordinates by Ren Descartes played an essential role in the development of algebra (geometric figures, such as plane curves, could now be represented by equations) and, later on, in the emergence of infinitesimal calculus in (17th century). For a long time, there was no clear distinction between physical space and geometrical space; starting with the discovery of non-Euclidean geometry (19th century) the notion of “geometric space” has undergone a radical transformation (up to the point that even notions like “space”, “point”, “line” etc lost their original intuitive content). The central question became: which “abstract” geometrical space best fits (models) the physical space. Differential Geometry: Contemporary geometry considers manifolds- which are spaces that approximately resemble the familiar Euclidean space only at small scales (e.g. spheres). On these, one considers various “geometric structures”, depending on the aspects one is interested in. Differential Geometry is the resulting study of manifolds endowed with such geometric structures. For instance, to talk about “lengths”, the geometric structure that one has to consider is known under the name of “Riemannian metric” and the resulting field is known as “Riemannian Geometry” (a subfield of Differential Geometry). Differential geometry is also the language in which Einstein’s general theory of relativity is expressed: the universe appears as a smooth manifold equipped with a pseudo-Riemannian metric, which describes the curvature of space-time; understanding this curvature is essential for the positioning of satellites into orbit around the earth. One may even say that each physical theory comes with its own (subfield of) geometry. Another example comes from the Hamiltonian formulation of classical mechanics, which gives rise to Poisson Geometry. In this theory, the objects that are studied are manifolds endowed with the geometric structures that allows one to write down Hamilton’s equations (“Poisson structures”). We also have to mention here that role played by symmetries in geometry. When looking at most of Eschers drawings, one realizes the presence of symmetry, which allows one to reconstruct the complete drawing from a smaller part of it. More generally, one of the central ideas in geometry is to understand (and even classify) the geometric objects via their ”symmetries”; this originates in Klein’s Erlanger Programm (1872). The precise mathematical notion that allows us to talk about symmetries in Differential Geometry is that of “Lie group”. Its birth goes back to the work of Sophus Lie on symmetries of differential equations (at the end of the nineteenth century) and that of Elie Cartan on symmetries of geometric structures (at the beginning of the twentieth century). Nowadays one talks about “Lie Theory”, which pervades modern mathematics and theoretical physics. Topology: A close relative of Geometry is the field of “Topology”, which is concerned with properties that are preserved under continuous deformations of objects, such as deformations that involve stretching, but no tearing or gluing. For instance, a circle and an ellipsis, although geometrically distinct, have the same topology: one can be obtained from the other by a continuous transformation- realise the ellipsis as the shadow of a non-horizontal circle and consider the transformation along the rays of light. Similarly, spheres and convex polyhedra are topologically similar; as a consequnce, one arrises at the famous theorem of Euler which says that, for any 13
Page 1: Curriculum Vitae for Marius Crainic
Page 5: Experience 2007- UHD , Utrecht Univ
Page 9 and 10: Talks in (international) conference
Page 11: Organizational activities • Poiss
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Page 19: At the border of research/teaching:
Page 22 and 23: Please see the web-page: http://www
Page 24: Other supervising experience 2011-2
Page 28 and 29: Publications 1. Main published pape
Page 30: Work in progress [1] Poisson manifo

Curriculum Vitae for Marius Crainic

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